What Are Learning Trajectories and How Does VKRP Use Them?

Understanding how children develop mathematical skills can be beneficial when planning for instruction and tracking growth over time. VKRP utilizes math learning trajectories to map out the progression of children’s mathematical understanding. Developed by Drs. Douglas Clements and Julie Sarama, these trajectories provide a structured approach to identifying and supporting children’s mathematical growth. By focusing on key areas such as geometry, patterning, numeracy, and computation, VKRP aims to enhance early math education and ensure that every child has the opportunity to succeed.

What are learning trajectories?

A learning trajectory describes “the order and nature of the steps in the growth of students; mathematical understanding, and about the nature of the instructional experiences that might support them in moving step-by-step toward the goals of the school mathematics” (Daro et al., 2011, p.12).

The math learning trajectories we focus on for VKRP have been developed by Drs. Douglas Clements and Julie Sarama. They describe a learning trajectory as having three parts: (1) a mathematical goal, (2) a developmental progression that describes what children know and can do mathematically, and (3) instructional activities (including tasks and teaching strategies) explicitly designed to promote forward movement to higher levels of the progression.

What topics do the learning trajectories cover?

There are 20 trajectories that cover the big ideas in early numeracy, geometry, and measurement.

What are the ways learning trajectories can support my classroom practice?

Learning trajectories can help teachers look for and make sense of mathematical behaviors that might otherwise go unnoticed. Importantly, learning trajectories can help teachers:

Describe what children know and can do mathematically – not just what children do not know or are not yet able to do.
Identify common errors or misconceptions across different levels of thinking.
Instructional activities that include productive scaffolds, as well as adjustments for children who need more support or greater challenge.

In general, learning trajectories are another resource that can help teachers think more flexibly and nimbly about how to elicit and respond to the mathematical ideas and representations of young children.

What are some of the things learning trajectories do not do?

Learning trajectories can enhance classroom practice, planning and decision-making, but do not replace curriculum. They also should not be used to diagnose mathematical difficulties or replace screening tools.

Where can I learn more about Learning Trajectories (LT)?

The Learning and Teaching with Learning Trajectories website has valuable videos and resources broken down by learning trajectory, updated under the guidance of Drs. Clements and Sarama.

Each LT contains:

A description of mathematical thinking and behaviors characteristic of each level of the developmental progression;
A video (or multiple videos) depicting what thinking looks like in situ;
Activities designed by teachers and teacher educators to help children cultivate the conceptual understanding and strategies that defines each level of the progression.

Importantly, there is a Focus Tool, which enables users to filter the trajectories by age/grade, as well as by standards and assessments.

We hope you have found this to be a useful explanation of the Math Learning Trajectories developed by Drs. Clements and Sarama and how they are used to highlight math skills covered in the Early Mathematics Assessment System (EMAS). Additional information about the VKRP math domains, subdomains, and skills can be found on the VKRP Webportal under Instructional Resources > Resources Overview.

Daro, P., Mosher, F. A., & Corcoran, T. B. (2011). Learning Trajectories in Mathematics: A Foundation for Standards, Curriculum, Assessment, and Instruction. 86.

More Questions for the VKRP Team? VKRP provides support via the online chat feature when you are in the system, via email vkrp@virginia.edu, and via toll free 866-301-8278